Grading Morgans

I would highly suggest PCGS (Professional Coin Grading Service). Their grading is generally very consistent and they're head to head with their rival NGC (Numismatic Grading Service).

PCGS is one of the two mosted trusted Third Party Graders ( TPG).

Here is their website: http://pcgs.com/

Here is their grading process video (slightly outdated, but it gets the job done): https://www.youtube.com/watch?v=VTCSndJXS48

They generally charge about $20 per coin to be graded, so if you have 50, that would cost about $1000. I would simply select the best of the best to submit, not just any random Morgan. (though this topic should be under Third Party Grading section or U.S. Classic Coins section)

PCGS's slabs are clear plastic, while NGC's slabs are a white plastic. Of course, they have PCGS and NGC multiple times on their slabs. PCGS has the new DuPont registry anti-counterfeit hologram, which is nice.

Edit: here is the PCGS photograde website, which you can use to grade your coins yourself to find the best of the best to send off: http://www.pcgs.com/Photograde/#//

Just curious, why do you need to have your Morgans graded/certified by a TPG service?

No, that is untrue. You can grade them yourself and determine the value. Though some prefer TPGs to make sure the coin is not a counterfeit/grade the coin for them.

You can also post some pictures to this site to get an idea of grades.